cs-123 — The Insurance Riddle
| Field | Value |
|---|---|
| id | cs-123 |
| difficulty | Intermediate |
| topics | expected value, risk |
| lecture | lecture-31 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | loops, lists, and tracing from lectures 1-6 |
| objective | choose the technique, trace it faithfully, and defend the boundary behaviour |
| solution | held by the instructor; discussed after the attempt |
Problem
Insurance costs more than expected loss. Why rational people still buy: variance, ruin, and utility in plain language. EV as a tool, not a god.
Your deliverable is the stated assumptions, the expected value computed for the worked instance, the ruin-aversion caveat stated, and one contested case. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: phone worth 600; loss chance 10%/year; premium 80
- Output: EV loss = 60 << 80 premium: 'bad deal' by EV; still rational for ruin-aversion - EV is a tool, not the verdict
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- EV says decline; utility says the 600 loss hurts more than linearly. The case is about knowing which model fits.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Propose one extra rule that would change the verdict — is it an improvement?"
Constraints and assumptions
- Difficulty: Intermediate (loops and lists assumed).
- Topics: expected value, risk.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes for the plan and trace; finishing the details is a bonus, defending the method is the target.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Compute the flip point where the decision changes and defend the threshold.